First of all, a warm welcome to Kinmunity, skyldir! It's great to see that you're open to your experiences to the point of wanting to find out what's behind. To open up the round of answers, I'd like to put forward that nobody can tell you who or what you are - it's finally up to you to find out. However, we'll be more than happy to provide help along the way.
I think it's quite obvious that you have at least a deep connection to birds and wolves. That's a good starting point. Combined with your feeling of having the wrong body it's a strong point to check the possibiliy of being a therian imo. Many therians I know would report very similar things as you did. You could also be what we call 'otherhearted'. Therians are (non-physically) identifying, in part or in whole,
as one or more non-human earth animals. Whereas otherhearted people are humans identifying
with or having an exceptionally strong connection to one or more non-human creatures. It's a bit fuzzy what "exceptionally strong" means, though.. in any case, it's more than just liking the animal. These are only very abridged definitions, though. I suggest to look up both terms by searching the site. There are plenty of reports and resources.
This article may be a good start.
I'd like to add that therian and otherhearted are just terms. They in no way change your experiences, and you don't have to "qualify" for one or the other. Your personal experiences are the reference; it's actually the terms that have to qualify for describing them correctly. Hence, I also advice to consider additional personal experiences. Do you have any quirks, unusual mental states, physical-like feelings, dreams or visions that relate to the feeling of being non-human or being wolf or bird? I'm obviously talking of "shifts" here. Did others maybe even notice your interest in these animals? Do you have any idea about a specific species of wolf / bird you could be or most strongly relate to? Considering these questions should help you getting a clearer picture. It's a long journey, so I wish you all the best in advance!